Tablo’s streaming functionality uses HLS. Because HLS is based on a series of short (typically 10 seconds) duration media files, there is an inherent need to have an initial delay before viewing while the first video segment is prepared. That’s the nature of the beast. IIRC Tablo has experimented with shorter length segments which do improve the “startup” time somewhat.
Tablo also transcodes the MPEG-2 broadcast stream into H.264, which also may account for some fraction of the delay. As far as I am aware HDHomerun simply uses the broadcast stream as-is.